Question

Netra a std X student is fond of reading

books. She wants to buy a book that costs

₹207.50. She has decided to save her

pocket money for the same. Netra saved ₹

50 in the 1st week and then increased her

weekly saving by ₹ 17.50.
i From the information given above, write the values of first term and

common difference.

ii Write the formula to determine the total amount saved by Netra.

iii In which week is it possible for her to buy the book?

iv Determine her saving in that week.

v Being a student of the same age group, what inspiration will you

take from Netra?




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Answer 1

Correct Question :- Netra a std X student is fond of reading books. She wants to buy a book that costs ₹202.50. She has decided to save her pocket money for the same. Netra saved ₹50 in the 1st week and then increased her weekly saving by ₹ 17.50.

To Find :-

1. From the information given above, write the values of first term and common difference.
2. Write the formula to determine the total amount saved by Netra.
3. In which week is it possible for her to buy the book ?
4. Determine her saving in that week. ?

Solution :-

→ Total cost of book = ₹202.50 = Sn

→ Money she saved in first week = ₹50 = first term = a .

→ Weekly increased saving = ₹ 17.50 = common difference = d .

Let us assume that , in nth week she saved money to buy book .

so,

→ Sn = (n/2)[2a + (n - 1)d]

→ 202.5 = (n/2)[2*50 + (n - 1)17.5]

→ 202.5 = (n/2)[100 + 17.5n - 17.5]

→ 405 = n(82.5 + 17.5n)

→ 405 = 82.5n + 17.5n²

→ 17.5n² + 82.5n - 405 = 0

→ 5(3.5n² + 16.5n - 81) = 0

→ 3.5n² + 16.5n - 81 = 0

→ (35/10)n² + (165/10)n - 81 = 0

→ (7/2)n² + (33/2)n - 81 = 0

→ 7n² + 33n - 162 = 0

→ 7n² - 21n + 54n - 162 = 0

→ 7n(n - 3) + 54(n - 3) = 0

→ (n - 3)(7n + 54) = 0

→ n = 3 or (-54/7)

Therefore , in 3rd week she saved money to buy book .

now,

→ an = a + (n - 1)d

→ an = 50 + (3 - 1)17.5

→ an = 50 + 2 * 17.5

→ an = 50 + 35

→ an = 85 .

Hence, her saving in that week is ₹85.

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